2/3w+3=1/6w+2

Solution for 2/3w+3=1/6w+2 equation:

2/3w+3=1/6w+2

We move all terms to the left:

2/3w+3-(1/6w+2)=0


Domain of the equation: 3w!=0

w!=0/3

w!=0

w∈R



Domain of the equation: 6w+2)!=0

w∈R


We get rid of parentheses

2/3w-1/6w-2+3=0

We calculate fractions


12w/18w^2+(-3w)/18w^2-2+3=0

We add all the numbers together, and all the variables

12w/18w^2+(-3w)/18w^2+1=0

We multiply all the terms by the denominator


12w+(-3w)+1*18w^2=0

Wy multiply elements

18w^2+12w+(-3w)=0

We get rid of parentheses

18w^2+12w-3w=0

We add all the numbers together, and all the variables

18w^2+9w=0

a = 18; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·18·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$w_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*18}=\frac{-18}{36}
=-1/2
$
$w_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*18}=\frac{0}{36}
=0
$